Magnetic Effects of Current and Magnetism

Definition

When a charge is stationary, it only produces an electric field. However, the moment it starts moving, it produces a magnetic field. If this moving charge enters an external magnetic field, it experiences a force.

Explanation

Imagine a magnetic field as a series of invisible "wind" lines. If a charged particle (like an electron) flies straight through these lines, the field "pushes" it sideways. The magnitude of this push depends on the velocity of the particle and the strength of the magnet.

• Lorentz Force: The total force experienced by a charge moving in both electric and magnetic fields.
• Direction: The force is always perpendicular to both the velocity of the charge and the magnetic field.
• Zero Force: If the charge moves parallel to the field, the force is zero.

Examples

• An electron moving perpendicularly into a uniform magnetic field will follow a circular path.
• A proton beam in a vacuum tube being deflected by a permanent magnet.

Real-Life Use

Cathode Ray Tube (CRT) Televisions: In older TVs, an electron gun fired a beam of electrons. Magnetic coils deflected these electrons up, down, left, and right to "paint" the image on the screen.

A. Velocity Selector

Meaning: A device that only allows particles of a specific velocity to pass through straight.

How it works: By applying both an electric field ($E$) and a magnetic field ($B$) perpendicular to each other, the forces can be balanced ($qE = qvB$). Only particles with $v = E/B$ move undeflected.

B. The Cyclotron

Meaning: A machine used to accelerate charged particles to very high energies.

Simple Explanation: A "spiral race track" where a magnetic field keeps the particle in a circle and an electric field provides "kicks" of speed at the gap between D-shaped electrodes.

Real-Life Use: Cancer Treatment

Proton Therapy: Cyclotrons produce radioisotopes and accelerate protons to destroy tumors with high precision, minimizing damage to surrounding healthy tissue.

A. Biot-Savart Law

Meaning: Describes the magnetic field generated by a small segment of current-carrying wire.

Key Concept: The magnetic field ($B$) depends on the current ($I$), the length of the wire segment, and the distance from the wire. The closer you are, the stronger the field.

B. Ampere’s Circuital Law

Meaning: A shortcut for finding the magnetic field for symmetrical objects. The line integral of the magnetic field around a closed loop is proportional to the total current passing through that loop.

Real-Life Use: MRI Machines

Magnetic Resonance Imaging (MRI): Uses the principles of Ampere's Law to create a powerful, uniform magnetic field across the body to image soft tissues like the brain.

Solenoid

Meaning: A long coil of wire wound closely in a helix. It acts exactly like a bar magnet with North and South poles when current flows.

Example: Internal coil in an electric bell.

Toroid

Meaning: A solenoid bent into a circle (doughnut shape). It traps the magnetic field inside the core, resulting in almost no external field.

Example: Toroidal cores in power transformers.

Real-Life Use: Junk Yard Electromagnets

A giant solenoid wrapped around an iron core is used to lift scrap cars. When current is OFF, the car is dropped.

Force between Parallel Currents

• Same direction: Wires attract each other.
• Opposite direction: Wires repel each other.

Torque on a Current Loop

When a current-carrying loop is placed in a magnetic field, the forces on opposite sides create a "turning effect" known as torque.

Real-Life Use: Electric Motors

Every electric motor (Fans, Mixers, Tesla cars) works on this principle. Current in a loop within a B-field creates torque, causing the motor to spin.

Meaning: An instrument used to detect very small currents in a circuit.

Working: A coil suspended between magnetic poles experiences torque when current flows, rotating a needle across a scale.

Application: Converting MCG to an Ammeter by adding a low-resistance "shunt" in parallel.

Earth's Magnetism

• Magnetic Declination: Angle between geographic north and magnetic north.
• Magnetic Dip (Inclination): Angle the magnetic needle makes with the horizontal plane.

Magnetic Properties Table

Real-Life Use: Data Storage

Hard drives use ferromagnetic materials to store binary data ($0$s and $1$s) by changing magnetization spots on a disk.

• Maglev Trains: Use powerful electromagnets to eliminate friction, reaching speeds > 600 km/h.
• LHC (Large Hadron Collider): Superconducting magnets bend proton beams to study the origin of the universe.
• EV Motors: High-efficiency Neodymium magnets convert battery power into motion.

Case Study: Proton Therapy System

In targeted cancer treatment, a Cyclotron ionizes hydrogen to create protons. Using a combination of uniform magnetic fields (to bend the path) and alternating electric fields (to accelerate), the protons spiral outward. These beams are steered using magnetic lenses to hit the tumor exactly at the Bragg Peak, destroying the cancer while leaving healthy brain tissue untouched.

1. What is the unit of magnetic field $B$?
   Ans: b) Tesla
2. A charged particle moving parallel to a magnetic field experiences a force of:
   Ans: c) Zero
3. Which rule finds the direction of force on a current-carrying conductor?
   Ans: b) Fleming's Left-hand rule
4. The magnetic field inside a long solenoid is:
   Ans: c) Uniform
5. Which of the following is a diamagnetic material?
   Ans: c) Bismuth
6. If the current in a solenoid is doubled, the magnetic field becomes:
   Ans: b) Double
7. The angle of dip at the magnetic equator is:
   Ans: a) $0^\circ$
8. Two parallel wires carrying current in opposite directions will:
   Ans: b) Repel each other
9. A galvanometer is converted into a voltmeter by:
   Ans: b) High resistance in series
10. The Curie temperature is the point where:
    Ans: b) Ferro becomes Para

1. Q: State Biot-Savart Law and its vector form.
   Ans: It states that $dB$ is proportional to current ($I$), length ($dl$), and $\sin\theta$, and inversely to $r^2$. Vector form: $dB = \frac{\mu_0}{4\pi} \frac{I(dl \times \hat{r})}{r^2}$.
2. Q: Explain the principle of a Velocity Selector.
   Ans: It uses crossed $E$ and $B$ fields. When $qE = qvB$, the net force is zero and the particle moves undeflected at $v = E/B$.
3. Q: Compare Dia, Para, and Ferro magnetic materials.
   Ans: Dia (repelled), Para (weakly attracted), Ferro (strongly attracted). Ferro loses properties above Curie Temp.
4. Q: What is the function of a soft iron core in an electromagnet?
   Ans: High permeability concentrates field lines, increasing strength and allowing quick demagnetization.
5. Q: Derive the force between two parallel conductors.
   Ans: Use $B_1 = \mu_0 I_1 / 2\pi d$ and $F = I_2 L B_1 \sin\theta$ to get $F/L = \mu_0 I_1 I_2 / 2\pi d$.
6. Q: Define Magnetic Declination and Dip.
   Ans: Declination is the angle between geographic and magnetic North. Dip is the angle between the total field and the horizontal plane.
7. Q: How does a Moving Coil Galvanometer work?
   Ans: A current-carrying loop in a uniform field experiences torque, causing deflection proportional to current.
8. Q: Why is a cyclotron not used for electrons?
   Ans: Due to low mass, electrons reach relativistic speeds quickly, changing their mass and orbit frequency.
9. Q: What is a Toroid?
   Ans: A circular solenoid that confines the magnetic field entirely within its core.
10. Q: Describe properties of magnetic field lines.
    Ans: They form closed loops, go from N to S, never intersect, and density shows field strength.

• Moving Charge $\rightarrow$ Magnetic Field.
• Solenoid $\approx$ Bar Magnet.
• Parallel Currents: Same $\rightarrow$ Attract, Opposite $\rightarrow$ Repel.

Mnemonics:

1. TFS (Left Hand Rule): Thumb $\rightarrow$ Thrust (Force), First Finger $\rightarrow$ Field, Second Finger $\rightarrow$ Strong Current.

2. D-P-F: Dia (Distanced/Repelled), Para (Partially attracted), Ferro (Full attraction).